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midterm_2_exam

# midterm_2_exam - MA 265 GOINS MIDTERM EXAMINATION#2...

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Unformatted text preview: MA 265 GOINS MIDTERM EXAMINATION #2 Instructions: Circle the correct answer on the follow- ing pages. You have 50 minutes to com- plete 25 problems. No textbooks, personal notes, calculators, or computing aids are allowed during the examination period. Each problem is worth 4 points. This examination is worth 100 points. Name: 1 2 MA 265 MIDTERM #2 Chapter 4. Real Vector Spaces 4.1: Vectors in the Plane and in 3-Space 1. Determine the head of the vector bracketleftbigg − 2 5 bracketrightbigg whose tail is ( − 3 , 2). A. (1 , − 3) B. ( − 1 , 3) C. ( − 5 , 7) D. None of the above 2. Determine the tail of the vector − 1 6 5 whose head is (4 , 6 , 2). A. (5 , , − 3) B. (3 , 12 , 7) C. ( − 5 , , 3) D. None of the above 3. For which pairs of points P and Q do we have −→ PQ = bracketleftbigg 2 3 bracketrightbigg ? i. P (0 , 0) and Q (3 , 2) ii. P (1 , 1) and Q (3 , 4) iii. P (2 , 2) and Q (4 , 6) A. (i) only B. (i) and (ii) C. (i), (ii), and (iii) D. None of the above 4.2: Vector Spaces 4. If V is a real vector space, then the scalar product c ⊙ u = only when c = 0. A. True B. False 5. Let V be the set of positive real num- bers. Define ⊕ by u ⊕ v = uv and ⊙ by c ⊙ v = c + v . Which of the following is true for all scalars c and all positive real numbers u , v , and w ?...
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midterm_2_exam - MA 265 GOINS MIDTERM EXAMINATION#2...

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